

This algorithm was discovered independently as
the Loris–Verhoeven algorithm [1]},
the primal–dual fixed point algorithm
based on proximity operator (PDFP\(^2\) O) [2]},
and the proximal alternating predictor corrector (PAPC) [3]}.
Comparison with (REF ) reveals a minor difference
between these two algorithms:
the gradient term in the \(z\) -update is taken at the newest primal
iterate \(x^{(k+1)}\)  in Loris–Verhoeven (REF )
and at the previous point \(x^{(k)}\)  in the shifted version.
This difference is inherited in the proximal gradient algorithm
and its shifted version (REF ).
